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Diffuse hydrogen gas within a galaxy may be assumed to follow a Maxwell distribution at temperature 106 K, while the temperature appropriate for the H gas in the inter-galactic space, following the same distribution, may be taken to be 104 K. The ratio of thermal broadening ΔvG / ΔvIG of the Lyman-α line from the H- atoms within the galaxy to that from the inter-galactic space is closest to
  • a)
    100
  • b)
    1/100
  • c)
    10
  • d)
    1/10
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Diffuse hydrogen gas within a galaxy may be assumed to follow a Maxwel...
For the hydrogen gas in the galaxy to the inter-galactic space can be determined using the following formula:

Ratio = (Temperature of Galaxy gas) / (Temperature of Inter-galactic gas)

= (106 K) / (104 K)

= 100

Therefore, the ratio of thermal broadening for the hydrogen gas in the galaxy to the inter-galactic space is 100.
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Diffuse hydrogen gas within a galaxy may be assumed to follow a Maxwel...
Concept:
The radiation damping broadening is negligible, so that, for all practical purposes the spread of the frequencies emitted by a collection of atoms in a gas is infinitesimally narrow. The observer, however, will not see an infinitesimally thin line. This is because of the motion of the particles in hot gas. Some atoms are moving hither, and the wavelength will be blue-shifted; others are moving on, and the wavelength will be red-shifted. The result will be a broadening of the lines, known as thermal broadening.
Calculation:
The expression for thermal broadening is given by
Δ ω = 2 ω(2kBT ln 2/Mc2)1/2
Thus Δ ω ∝ T1/2
Diffuse hydrogen gas within a galaxy may be assumed to follow a Maxwell distribution at temperature 106 K
The temperature appropriate for the H gas in the inter-galactic space is taken to be 104 K
Thus 
Δ ω1 : Δ ω2 = (106 : 104)1/2
∴ Δ ω1 : Δ ω2  = 10
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Diffuse hydrogen gas within a galaxy may be assumed to follow a Maxwell distribution at temperature 106 K, while the temperature appropriate for the H gas in the inter-galactic space, following the same distribution, may be taken to be 104 K. The ratio of thermal broadening ΔvG / ΔvIG of the Lyman-α line from the H- atoms within the galaxy to that from the inter-galactic space is closest toa)100b)1/100c)10d)1/10Correct answer is option 'C'. Can you explain this answer?
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